Characterization of continuous orbit-equivalence classes

Characterize the continuous orbit-equivalence class of free minimal dynamical systems beyond the cases covered by the known rigidity results for -actions and odometers.

Background

The paper discusses continuous orbit equivalence (COE) as a classification relation for dynamical systems and notes that, although some rigidity results are known for particular acting groups and for odometers, a general description of COE classes is unavailable. Such a characterization would clarify which systems can be continuously orbit equivalent and would extend the structural understanding developed for equicontinuous systems and odometers.